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Q.

The $\frac{p}{q}$ form of the number $0. \bar{9}$ is

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a

\frac{9}{10}

b

\frac{9}{100}

c

\frac{1}{9}

d

1

answer is D.

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Detailed Solution

Let $x = 0. \bar{9}$

$= 0.999 \dots$

$10 x = 10 \times 0.999 \dots [∵ Periodicity = 1]$

Question Image

$9 x = 9$

$x = \frac{9}{9} = 1 \Rightarrow x = 1$

$∴ 0. \bar{9} = 1$

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